Growth of solutal dendrites—A cellular automaton model

Abstract

The stochastic cellular automaton (CA) model, originally proposed by Dilthey et al. (1997) was further refined and applied to the simulation of dendritic growth controlled by solutal effects in the low Péclet number regime. The use of square cells in the division of the computational domain introduces an artificial anisotropy when growth is simulated by capture of the closest neighboring cells. This artificial anisotropy becomes significant when the preferential growth direction is not aligned with the axis of the cell. The proposed model offers a solution for the artificial anisotropy using a new set of capturing rules. It also recommends a stability parameter whose value must converge to the stability constant, σ*, to enable the CA model to predict steady-state dendritic growth kinetics. The model reproduces qualitatively most of the dendritic features observed experimentally, such as secondary and tertiary branching, parabolic tip, arms generation and selection. Validation was performed by comparing the simulated secondary dendrite arm spacing with literature values and then by comparing the predictions of the classic Lipton-GIicksman-Kurz theory for steady state tip velocity, with simulated values as function of melt undercooling. Both comparisons were found to be in good agreement. However, results are still mesh dependent.